## The duality principle and its application to optimal control of linear systems |

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### Contents

MINIMUM NORM PROBLEMS IN BANACH SPACES | 7 |

KINIMAX CONTROL FOR DISCRETE TIKE SYSTEMS | 43 |

with Fixed Terminal Condition | 62 |

### Common terms and phrases

alignment relation Banach space bang-bang bounded linear functional bounded linear operator Cauchy sequence chapter Computing The Dual conditionally reflexive conjugate operator conjugate space constraint Continuous Time System Control for Continuous control for discrete convex set corresponding dual problem criterion 3-2 Definition denoted desired trajectory discrete time systems discussed duality principle existence finite dimensional Fixed-Terminal following form Free-Terminal functional F given vector Hahn-Banach theorem hence inequality linear discrete-time system linear operator mapping linear system linear vector space max max maximum principle minimax control problems minimizes the primal minimum norm problem normed linear space normed linear vector normed space obtain the optimal optimal control optimal element optimal solution optimal vectors orthogonal subspace performance criterion primal problem product space Proof Proposition real number single space solved space is defined sublinear functional transformed variables vector function spaces vQ(t vr(k yd(k